The common measures of center or measures of central tendency are the mean, median and mode
For the mean we have the common average called arithmetic mean simply sum of all values divided by the total number of values. We have the population mean denoted by #mu# and sample mean denoted by #barx# the definitional formulas are
#mu = (sumx)/N and barx =(sumx)/n#
While median is the middle observation of an arrayed data. Meaning median is a positional measure. That is denoted by #mu_d or Md#
if the number of observation is odd:
#mu_d = x_[(n+1)/2]# and if the number of observation is even
#mu_d = (x_(n/2)+x_(n/2+1))/2# for illustrative example find the median of the given scores: 2, 7, 8, 1, 4, 5
First thing to do is make an array. That is to arrange the data from least-to-greatest or greatest-to-least.
Array: 1, 2, 4, 5, 7, 8
Next step: since the number of observation is even (6) use the appropriate formula that is
#mu_d = (x_(n/2)+x_(n/2+1))/2=(x_(6/2)+x_(6/2+1))/2 = (x_3+x_4)/2#
it tells that you need to add the 3rd and 4th observations and divide it by two.
Now we have
#mu_d = (4+5)/2 = 4.5# Therefore the median score is 4.5.
Lastly, mode is the most observed value or values. That is denoted by #mu_o or Mo#. For example,
Find the modal score of the given set: 1, 1, 2, 2, 4, 5, 5, 5
5 is the most observed value therefore Mo = 5. Another example find the modal score of the set: 1, 1, 1, 2, 2, 2, 3, 3,3
Since each observation (1 , 2, 3) appears thrice, there is no mode. There is no most observed value.
Note if a set has exactly one mode then the set is unimodal, if there is two modes say for the set: 1, 1, 2, 3, 3 the modes are 1 and 3 then, this set is bimodal. A set can also be trimodal or multimodal.
Supplementary: Geometric mean, harmonic mean. Hope this help.